Related papers: A flexible and interpretable spatial covariance mo…
This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is…
Graphical models are commonly used to represent conditional dependence relationships between variables. There are multiple methods available for exploring them from high-dimensional data, but almost all of them rely on the assumption that…
The advent of data science has provided an increasing number of challenges with high data complexity. This paper addresses the challenge of space-time data where the spatial domain is not a planar surface, a sphere, or a linear network, but…
This paper is the second in a series of papers which combine graphical modelling and marked spatial point patterns. Extending the previous results of \cite Eckardt (2016a), we introduce a marked spatial dependence graph model which depicts…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
Models for areal data are traditionally defined using the neighborhood structure of the regions on which data are observed. The unweighted adjacency matrix of a graph is commonly used to characterize the relationships between locations,…
Graphical models are widely used in diverse application domains to model the conditional dependencies amongst a collection of random variables. In this paper, we consider settings where the graph structure is covariate-dependent, and…
When modeling geostatistical or areal data, spatial structure is commonly accommodated via a covariance function for the former and a neighborhood structure for the latter. In both cases the resulting spatial structure is a consequence of…
The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space-time data arising from climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance…
We present a new method for constructing valid covariance functions of Gaussian processes for spatial analysis in irregular, non-convex domains such as bodies of water. Standard covariance functions based on geodesic distances are not…
In this work we present full Bayesian inference for a new flexible nonseparable class of cross-covariance functions for multivariate spatial data. A Bayesian test is proposed for separability of covariance functions which is much more…
Spatial-temporal graph modeling is an important task to analyze the spatial relations and temporal trends of components in a system. Existing approaches mostly capture the spatial dependency on a fixed graph structure, assuming that the…
Recent studies have shown great promise in applying graph neural networks for multivariate time series forecasting, where the interactions of time series are described as a graph structure and the variables are represented as the graph…
This article proposes methods to model nonstationary temporal graph processes. This corresponds to modelling the observation of edge variables (relationships between objects) indicating interactions between pairs of nodes (or objects)…
The second-order, small-scale dependence structure of a stochastic process defined in the space-time domain is key to prediction (or kriging). While great efforts have been dedicated to developing models for cases in which the spatial…
We introduce a novel class of non-stationary covariance functions for random fields on linear networks that allows both the variance and the correlation range of the random field to vary spatially. The proposed covariance functions are…
In the analysis of multivariate spatial and univariate spatio-temporal data, it is commonly recognized that asymmetric dependence may exist, which can be addressed using an asymmetric (matrix or space-time, respectively) covariance function…
In geostatistics, it is common to model spatially distributed phenomena through an underlying stationary and isotropic spatial process. However, these assumptions are often untenable in practice because of the influence of local effects in…
The conditional autoregressive model is a routinely used statistical model for areal data that arise from, for instances, epidemiological, socio-economic or ecological studies. Various multivariate conditional autoregressive models have…
Multivariate geostatistics is based on modelling all covariances between all possible combinations of two or more variables at any sets of locations in a continuously indexed domain. Multivariate spatial covariance models need to be built…